A convergence analysis of distributed dictionary learning based on the K-SVD algorithm

This paper provides a convergence analysis of a recent distributed algorithm, termed cloud K-SVD, that solves the problem of data-adaptive representations for big, distributed data. It is assumed that a number of geographically-distributed, interconnected sites have massive local data and they are collaboratively learning a sparsifying dictionary underlying these data using cloud K-SVD. This paper provides a rigorous analysis of cloud K-SVD that gives insights into its properties as well as deviations of the dictionaries learned at individual sites from a centralized solution in terms of different measures of local/global data and topology of the interconnections.